相关论文: Geodesic models generated by Lie symmetries

A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…

Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution,…

Arnold showed that the Euler equations of an ideal fluid describe geodesics on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the…

We derive the Lie and the Noether conditions for the equations of motion of a dynamical system in a $n-$dimensional Riemannian space. We solve these conditions in the sense that we express the symmetry generating vectors in terms of the…

This paper uses Lie symmetry analysis to investigate the biharmonic heat equation on a generalized surface of revolution. We classify the Lie point symmetries associated with this equation, allowing for the identification of surfaces and…

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime. We are interested in point transformations…

Simple homogeneous shear flows of frictionless, deformable particles are studied by particle simulations at large shear rates and for differently soft, deformable particles. The particle stiffness sets a time-scale that can be used to scale…

We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions…

We study the effects of pressure anisotropy and heat dissipation in a spherically symmetric radiating star undergoing gravitational collapse. An exact solution of the Einstein field equations is presented in which the model has a…

We present a new class of solutions to Einstein equations for the spherical collapse of dustlike matter coupled with heat flux. In this family of solutions spacetime shear is necessarily non-zero. Also these solutions have an interesting…

We consider a geodesic flow on a compact manifold endowed with a Riemannian (or Finsler, or Lorentz) metric satisfying some generic, explicit conditions. We couple the geodesic flow with a time-dependent potential, driven by an external…

The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to the uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The…

In this note we study the thermodynamic formalism for the positive geodesic flow on the modular surface. We define the pressure and prove the variational principle. We also establish conditions for the the pressure to be real analytic and…

We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…

Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…

Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…

We investigate insterstellar gas spheres by determining the metric functions, the material distribution, and the features of particle orbits in terms of stability and geodesics. An exact solution of the Einstein's equations for interstellar…

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of…

Some dynamical aspects of gravitational collapse are explored in this paper. A time-dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like…

The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive…